U.S. Pat. No. 5,987,189A discloses a method of combining height profiles of adjacent sections of a test surface to produce a composite profile of the surface and consists of taking successive measurements of adjacent sections of the surface of the test sample by sequentially placing them within the field of view of the instrument and profiling them by phase shifting or vertical scanning. The x-y translation of the microscope between successive measurements from one section to the next adjacent section of the surface being profiled is carried out by overlapping such sections, so that spatial continuity is maintained between measurements. The height data generated for each section are then combined to form a larger image corresponding to the entire surface tested and discontinuities and/or errors introduced by the x-y translation process are corrected by normalizing the overlapping portions to a common reference plane.
A plane is fitted through each set of measured heights in the overlapping regions and the tip, tilt and offset of each fitted plane are corrected to produce matching overlapping height data in adjacent sections. The measured height data for the balance of each section are then also corrected by the same difference in tip, tilt and offset to obtain a continuous normalized image.
An optical measuring system will have height drift because of heating and expansion of the optical components and/or sample, from the moment of switch on of the illumination or by variation in the environment temperature.
As time passes, the height drift may stabilize as the system and/or sample approaches thermal equilibrium. To avoid height drift effects, normal operation of an optical system (but not in the sample unless the sample is warmed up as well over all locations to be measured); however this takes a large amount of time.
Drift may have other causes as well, such as:    Ambient or instrument vibration    Instability in the ambient measurement environment (e.g. variations in ambient air temperature, air pressure, or in other applicable factors)    System creepIn such a situation height stability will never be achieved completely and always some drift will remain which cannot be pre-empted by instrument warm-up.
When fields are combined to measure a height map of a work piece larger than one field of view (FOV), drift will result in height offsets between the individual fields of view. An example may be found in a simulated measurement of an optical flat. The measurement is started from the lower left field of view and proceeds sequentially (See the measurement sequence in FIG. 1). The simulated individual FOV measurements are shown in FIG. 2.
Depending on the degrees of freedom in the combining algorithm, original global tilt and global orientation of the surface might be lost. Subsequently, the reconstruction of the global tilt and global orientation may be done by fitting a plane, for instance in a least-squares sense, to the individual measured fields. Depending on the measurement order (routing) the height offsets induced by the drift will then result in a global tilt error of the final result. An example of such a tilt error is shown in FIG. 3, which are the simulated results of stitching or combining the dataset of FIG. 2.